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arXiv · 2509.26194

Representation Theory of $0$-Schur Algebras and Related Categories

Woo-Seok Jung·Young-Tak Oh
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Abstract

Jensen, Su, and Yang described the projective indecomposable modules of the $0$-Schur algebra $\mathbf{S}_0(n,r)$ using its geometric realization. In this paper, the simple modules of $\mathbf{S}_0(n,r)$ are identified by computing the tops of the projective indecomposable modules. Furthermore, functorial relations among the module categories $\mathbf{H}_r(0)$\textsf{-mod}, $\mathbf{S}_0(n,r)$\textsf{-mod}, and $U_0(\mathfrak{gl}_n)$\textsf{-mod} are examined, where $\mathbf{H}_r(0)$ denotes the $0$-Hecke algebra and $U_0(\mathfrak{gl}_n)$ denotes the degenerate quantum group.

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Woo-Seok Jung, Young-Tak Oh. 2025-09-30. Representation Theory of $0$-Schur Algebras and Related Categories. https://arxiv.org/abs/2509.26194

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